Tunneling into the Edge of a Compressible Quantum Hall State

Abstract

We present a composite-fermion theory of tunneling into the edge of a compressible quantum Hall system. The tunneling conductance is non-Ohmic, due to slow relaxation of electromagnetic and Chern-Simons field disturbances caused by the tunneling electron. Universal results are obtained in the limit of a large number of channels involved in the relaxation. The tunneling exponent is found to be a continuous function of the Hall resistivity ${\ensuremath{\rho}}_{\mathrm{xy}}$, with a slope that is discontinuous at filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$, in the limit of vanishing bulk resistivity ${\ensuremath{\rho}}_{\mathrm{xx}}$. When $\ensuremath{\nu}$ corresponds to a principal fractional quantized Hall state, our results agree with the chiral Luttinger liquid theories of Wen and Kane, Fisher, and Polchinski.